   Chapter 11.4, Problem 10E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# If  s = 2 π r ( r + h ) ,  find  d r / d t  when r = 2 , h = 8 ,   d h / d t = 3 ,  and  d s / d t = 10 π .

To determine

To calculate: The value of drdt if s=2πr(r+h) for r=2,h=8,dhdt=3anddsdt=10π.

Explanation

Given Information:

The provided equation is:

s=2πr(r+h)

Formula used:

According to the chain rule, if f and g are differentiable functions with y=f(u) and u=g(x), then y is a differentiable function of x and:

dydx=dydududx

Calculation:

Consider the provided equation:

s=2πr(r+h)

Now, differentiate both sides with respect to t to get:

dsdt=ddt[2πr(r+h)]

Now, use the chain rule:

dydx=dydududx

To obtain the derivative of randh as:

dsdt=ddt[2πr(r+h)]dsdt=2πr(drdt+dhdt)+2π(r+h)drdt

Now, the provided values are r=2,h=8,dhdt=3anddsdt=10π

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